Multi-scale simulations predict responses to non-invasive nerve root stimulation

Central and Peripheral Motor Conduction Studies by Single-Pulse Magnetic Stimulation

Single-pulse magnetic stimulation is the simplest type of transcranial magnetic stimulation (TMS). Muscle action potentials induced by applying TMS over the primary motor cortex are recorded with surface electromyography electrodes, and they are called motor-evoked potentials (MEPs). The amplitude and latency of MEPs are used for various analyses in clinical practice and research. The most commonly used parameter is the central motor conduction time (CMCT), which is measured using motor cortical and spinal nerve stimulation. In addition, stimulation at the foramen magnum or the conus medullaris can be combined with conventional CMCT measurements to evaluate various conduction parameters in the corticospinal tract more precisely, including the cortical-brainstem conduction time, brainstem-root conduction time, cortical-conus motor conduction time, and cauda equina conduction time. The cortical silent period is also a useful parameter for evaluating cortical excitability. Single-pulse magnetic stimulation is further used to analyze not only the central nervous system but also the peripheral nervous system, such as for detecting lesions in the proximal parts of peripheral nerves. In this review article we introduce four types of single-pulse magnetic stimulation-of the motor cortex, spinal nerve, foramen magnum, and conus medullaris-that are useful for the diagnosis, elucidation of pathophysiology, and evaluation of clinical conditions and therapeutic effects. Single-pulse magnetic stimulation is a clinically useful technique that all neurologists should learn.

Transsynaptic activation of human lumbar spinal motoneurons by transvertebral magnetic stimulation

Noninvasive spinal stimulation has been increasingly used in research on motor control and neurorehabilitation. Despite advances in percutaneous electrical stimulation techniques, magnetic stimulation is not as commonly used as electrical stimulation. Therefore, it is still under discussion what neuronal elements are activated by magnetic stimulation of the human spinal cord. In this study, we demonstrated that transvertebral magnetic stimulation (TVMS) induced transsynaptic activation of spinal motoneuron pools in the lumbar cord. In healthy humans, paired-pulse TVMS was given over an intervertebral space between the L1-L2 vertebrae with an interpulse interval of 100 ms, and the stimulus-evoked electromyographic (EMG) responses were recorded in the lower limb muscles. The results show that the evoked EMG responses after the 2nd pulse were clearly suppressed compared with the widespread responses evoked after the 1st pulse in the muscles of the lower extremity, indicating that the transsynaptic activation of spinal motoneurons by the 2nd pulse was suppressed by the effects produced by the 1st pulse. The inconsistent modulation of response suppression to stimulus intensity across individuals suggests that the TVMS-evoked EMG responses are composed of the compound potentials mediated by the direct activation of motor axons and the transsynaptic activation of motoneuron pools through sensory afferents and that the recruitment order of those fibers by TVMS may be nonhomogeneous across individuals.

A systematic review of computational models for the design of spinal cord stimulation therapies: from neural circuits to patient-specific simulations

Seventy years ago, Hodgkin and Huxley published the first mathematical model to describe action potential generation, laying the foundation for modern computational neuroscience. Since then, the field has evolved enormously, with studies spanning from basic neuroscience to clinical applications for neuromodulation. Computer models of neuromodulation have evolved in complexity and personalization, advancing clinical practice and novel neurostimulation therapies, such as spinal cord stimulation. Spinal cord stimulation is a therapy widely used to treat chronic pain, with rapidly expanding indications, such as restoring motor function. In general, simulations contributed dramatically to improve lead designs, stimulation configurations, waveform parameters and programming procedures and provided insight into potential mechanisms of action of electrical stimulation. Although the implementation of neural models are relentlessly increasing in number and complexity, it is reasonable to ask whether this observed increase in complexity is necessary for improved accuracy and, ultimately, for clinical efficacy. With this aim, we performed a systematic literature review and a qualitative meta-synthesis of the evolution of computational models, with a focus on complexity, personalization and the use of medical imaging to capture realistic anatomy. Our review showed that increased model complexity and personalization improved both mechanistic and translational studies. More specifically, the use of medical imaging enabled the development of patient-specific models that can help to transform clinical practice in spinal cord stimulation. Finally, we combined our results to provide clear guidelines for standardization and expansion of computational models for spinal cord stimulation.

A Huygens' surface approach to rapid characterization of peripheral nerve stimulation

PURPOSE

Peripheral nerve stimulation (PNS) modeling has a potential role in designing and operating MRI gradient coils but requires computationally demanding simulations of electromagnetic fields and neural responses. We demonstrate compression of an electromagnetic and neurodynamic model into a single versatile PNS matrix (P-matrix) defined on an intermediary Huygens' surface to allow fast PNS characterization of arbitrary coil geometries and body positions.

METHODS

The Huygens' surface approach divides PNS prediction into an extensive pre-computation phase of the electromagnetic and neurodynamic responses, which is independent of coil geometry and patient position, and a fast coil-specific linear projection step connecting this information to a specific coil geometry. We validate the Huygens' approach by performing PNS characterizations for 21 body and head gradients and comparing them with full electromagnetic-neurodynamic modeling. We demonstrate the value of Huygens' surface-based PNS modeling by characterizing PNS-optimized coil windings for a wide range of patient positions and poses in two body models.

RESULTS

The PNS prediction using the Huygens' P-matrix takes less than a minute (instead of hours to days) without compromising numerical accuracy (error ≤ 0.1%) compared to the full simulation. Using this tool, we demonstrate that coils optimized for PNS at the brain landmark using a male model can also improve PNS for other imaging applications (cardiac, abdominal, pelvic, and knee imaging) in both male and female models.

CONCLUSION

Representing PNS information on a Huygens' surface extended the approach's ability to assess PNS across body positions and models and test the robustness of PNS optimization in gradient design.

Evaluation of Peripheral Electrostimulation Thresholds in Human Model for Uniform Magnetic Field Exposure

The external field strength according to the international guidelines and standards for human protection are derived to prevent peripheral nerve system pain at frequencies from 300-750 Hz to 1 MHz. In this frequency range, the stimulation is attributable to axon electrostimulation. One limitation in the current international guidelines is the lack of respective stimulation thresholds in the brain and peripheral nervous system from in vivo human measurements over a wide frequency range. This study investigates peripheral stimulation thresholds using a multi-scale computation based on a human anatomical model for uniform exposure. The nerve parameters are first adjusted from the measured data to fit the peripheral nerve in the trunk. From the parameters, the external magnetic field strength to stimulate the nerve was estimated. Here, the conservativeness of protection limits of the international guidelines and standards for peripheral stimulation was confirmed. The results showed a margin factor of 4-6 and 10-24 times between internal and external protection limits of Institute of Electrical and Electronics Engineers standard (IEEE C95.1) and International Commission on Non-Ionizing Radiation Protection guidelines, with the computed pain thresholds.

The Influence of Electrode Configuration Changes on the Sensory and Motor Response During (Re)Programming in Sacral Neuromodulation

OBJECTIVES

This study aimed to assess the neurophysiological basis behind troubleshooting in sacral neuromodulation (SNM). Close follow-up of SNM patients with program parameter optimization has proven to be paramount by restoring clinical efficacy and avoiding surgical revision.

MATERIALS AND METHODS

A total of 34 successful SNM patients (28 overactive bladder wet, six nonobstructive urinary retention) with an implantable pulse generator were included. All possible bipolar and monopolar electrode settings were tested at sensory threshold (ST) to evaluate sensory (mapped on a perineal grid with 1 cm² coordinates) and motor (peak-to-peak amplitude and latency of muscle action potential) responses of the pelvic floor. Pelvic floor muscle electromyography was recorded using a multiple array probe, placed intravaginally. Parametric tests were used for paired data: repeated-measures ANOVA or t-test. A nonparametric test was used for paired data: Friedman ANOVA or Wilcoxon signed rank (WSR) test; p < 0.05 was considered statistically significant. If significant, ANOVA was followed by Dunn-Bonferroni post hoc analysis.

RESULTS

Monopolar configurations showed significantly lower STs-1.38 ± 0.73 V vs 1.76 ± 0.89 V (paired t-test: p < 0.0001)-and presented with significantly higher peak-to-peak amplitudes-115.67 ± 79.03 μV vs 90.77 ± 80.55 μV (WSR: p = 0.005)-than bipolar configurations. When polarity was swapped, configurations with the cathode distal to the anode showed significantly lower STs, 1.73 ± 0.91 V vs 1.85 ± 0.87 V (paired t-test: p = 0.003), and mean peak-to-peak amplitudes, 81.32 ± 72.82 μV vs 100.21 ± 90.22 μV (WSR: p = 0.0001). Cathodal changes resulted in more changes in sensory responses than anodal changes (χ² test: p = 0.044). In cathodal changes only, peak-to-peak amplitudes were significantly higher when the distance between electrodes was maximally spread (WSR: p = 0.046).

CONCLUSIONS

From a neurophysiological point of view, monopolar configurations stimulated more motor nerve fibers at lower STs, therefore providing more therapeutic efficiency. Swapping polarity or changing the position of the cathode led to different sensory and motor responses, serving as potential reprogramming options.

Optimizing selective stimulation of peripheral nerves with arrays of coils or surface electrodes using a linear peripheral nerve stimulation metric

OBJECTIVE

We present a PNS oracle, which solves these computation time and linearity problems and is, therefore, well-suited for fast optimization of voltage distributions in contact electrode arrays and current drive patterns in non-contact magnetic coil arrays.

APPROACH

The PNS oracle metric for a nerve fiber is computed from an electric field map using only linear operations (projection, differentiation, convolution, scaling). Due to its linearity, this PNS metric can be precomputed for a set of coil or electrode segments, allowing rapid PNS prediction and comparison of any possible coil or electrode stimulation configuration constructed from this set. The PNS oracle is closely related to the classical activating function and modified driving functions but is adjusted to better correlate with full neurodynamic modeling of myelinated mammalian nerves.

MAIN RESULTS

We validated the PNS oracle in three MRI gradient coils and two body models and found good correlation between the PNS oracle and the full neurodynamic modeling approach (R ²  >  0.995). Finally, we demonstrated its potential utility by optimizing the driving currents and voltages of arrays of 108 magnetic coils or 108 contact electrodes to selectively stimulate target nerves in the lower leg.

SIGNIFICANCE

Peripheral nerve stimulation (PNS) by electromagnetic fields can be accurately simulated using coupled electromagnetic and neurodynamic modeling. Such simulations are slow and non-linear in the electric field, which makes it difficult to iteratively optimize coil and electrode configurations or drive patterns aiming to avoid PNS or to initiate it for therapeutic purposes.

Corticomotoneuronal Model for Intraoperative Neurophysiological Monitoring During Direct Brain Stimulation

Intraoperative neurophysiological monitoring during brain surgery uses direct cortical stimulation to map the motor cortex by recording muscle activity induced by the excitation of alpha motor neurons (MNs). Computational models have been used to understand local brain stimulation. However, a computational model revealing the stimulation process from the cortex to MNs has not yet been proposed. Thus, the aim of the current study was to develop a corticomotoneuronal (CMN) model to investigate intraoperative stimulation during surgery. The CMN combined the following three processes into one system for the first time: (1) induction of an electric field in the brain based on a volume conductor model; (2) activation of pyramidal neuron (PNs) with a compartment model; and (3) formation of presynaptic connections of the PNs to MNs using a conductance-based synaptic model coupled with a spiking model. The implemented volume conductor model coupled with the axon model agreed with experimental strength-duration curves. Additionally, temporal/spatial and facilitation effects of CMN synapses were implemented and verified. Finally, the integrated CMN model was verified with experimental data. The results demonstrated that our model was necessary to describe the interaction between frequency and pulses to assess the difference between low-frequency and multi-pulse high-frequency stimulation in cortical stimulation. The proposed model can be used to investigate the effect of stimulation parameters on the cortex to optimize intraoperative monitoring.

Mapping the current flow in sacral nerve stimulation using computational modelling

Sacral nerve stimulation (SNS) is an established treatment for faecal incontinence involving the implantation of a quadripolar electrode into a sacral foramen, through which an electrical stimulus is applied. Little is known about the induced spread of electric current around the SNS electrode and its effect on adjacent tissues, which limits optimisation of this treatment. The authors constructed a 3-dimensional imaging based finite element model in order to calculate and visualise the stimulation induced current and coupled this to biophysical models of nerve fibres. They investigated the impact of tissue inhomogeneity, electrode model choice and contact configuration and found a number of effects. (i) The presence of anatomical detail changes the estimate of stimulation effects in size and shape. (ii) The difference between the two models of electrodes is minimal for electrode contacts of the same length. (iii) Surprisingly, in this arrangement of electrode and neural fibre, monopolar and bipolar stimulation induce a similar effect. (iv) Interestingly when the active contact is larger, the volume of tissue activated reduces. This work establishes a protocol to better understand both therapeutic and adverse stimulation effects and in the future will enable patient-specific adjustments of stimulation parameters.

Sensitivity analysis of neurodynamic and electromagnetic simulation parameters for robust prediction of peripheral nerve stimulation

Peripheral nerve stimulation (PNS) has become an important limitation for fast MR imaging using the latest gradient hardware. We have recently developed a simulation framework to predict PNS thresholds and stimulation locations in the body for arbitrary coil geometries to inform the gradient coil optimization process. Our approach couples electromagnetic field simulations in realistic body models to a neurodynamic model of peripheral nerve fibers. In this work, we systematically analyze the impact of key parameters on the predicted PNS thresholds to assess the robustness of the simulation results. We analyze the sensitivity of the simulated thresholds to variations of the most important simulation parameters, including parameters of the electromagnetic field simulations (dielectric tissue properties, body model size, position, spatial resolution, and coil model discretization) and parameters of the neurodynamic simulation (length of the simulated nerves, position of the nerve model relative to the extracellular potential, temporal resolution of the nerve membrane dynamics). We found that for the investigated setup, the subject-dependent parameters (e.g. tissue properties or body size) can affect PNS prediction by up to ~26% when varied in a natural range. This is in accordance with the standard deviation of ~30% reported in human subject studies. Parameters related to numerical aspects can cause significant simulation errors (>30%), if not chosen cautiously. However, these perturbations can be controlled to yield errors below 5% for all investigated parameters without an excessive increase in computation time. Our sensitivity analysis shows that patient-specific parameter fluctuations yield PNS threshold variations similar to the variations observed in experimental PNS studies. This may become useful to estimate population-average PNS thresholds and understand their standard deviation. Our analysis indicates that the simulated PNS thresholds are numerically robust, which is important for ranking different MRI gradient coil designs or assessing different PNS mitigation strategies.

High-Resolution Multi-Scale Computational Model for Non-Invasive Cervical Vagus Nerve Stimulation

OBJECTIVES

To develop the first high-resolution, multi-scale model of cervical non-invasive vagus nerve stimulation (nVNS) and to predict vagus fiber type activation, given clinically relevant rheobase thresholds.

METHODS

An MRI-derived Finite Element Method (FEM) model was developed to accurately simulate key macroscopic (e.g., skin, soft tissue, muscle) and mesoscopic (cervical enlargement, vertebral arch and foramen, cerebral spinal fluid [CSF], nerve sheath) tissue components to predict extracellular potential, electric field (E-Field), and activating function along the vagus nerve. Microscopic scale biophysical models of axons were developed to compare axons of varying size (Aα-, Aβ- and Aδ-, B-, and C-fibers). Rheobase threshold estimates were based on a step function waveform.

RESULTS

Macro-scale accuracy was found to determine E-Field magnitudes around the vagus nerve, while meso-scale precision determined E-field changes (activating function). Mesoscopic anatomical details that capture vagus nerve passage through a changing tissue environment (e.g., bone to soft tissue) profoundly enhanced predicted axon sensitivity while encapsulation in homogenous tissue (e.g., nerve sheath) dulled axon sensitivity to nVNS.

CONCLUSIONS

These findings indicate that realistic and precise modeling at both macroscopic and mesoscopic scales are needed for quantitative predictions of vagus nerve activation. Based on this approach, we predict conventional cervical nVNS protocols can activate A- and B- but not C-fibers. Our state-of-the-art implementation across scales is equally valuable for models of spinal cord stimulation, cortex/deep brain stimulation, and other peripheral/cranial nerve models.

Modeling the pelvic region for non-invasive pelvic intraoperative neuromonitoring

Finite element analysis (FEA) of electric current distribution in the pelvis minor may help to assess the usability of non-invasive surface stimulation for continuous pelvic intraoperative neuromonitoring. FEA requires generation of quality volumetric tetrahedral mesh geometry. This study proposes the generation of a suitable mesh based on MRI data. The resulting volumetric mesh models the autonomous nerve structures at risk during total mesorectal excision. The model also contains the bone, cartilage, fat, skin, muscle tissues of the pelvic region, and a set of electrodes for surface stimulation. The model is ready for finite element analysis of the discrete Maxwell’s equations.

Low-frequency electrical dosimetry: research agenda of the IEEE International Committee on Electromagnetic Safety

This article treats unsettled issues in the use of numerical models of electrical dosimetry as applied to international limits on human exposure to low-frequency (typically  <  100 kHz) electromagnetic fields and contact current. The perspective in this publication is that of Subcommittee 6 of IEEE-ICES (International Committee on Electromagnetic Safety) Technical Committee 95. The paper discusses 25 issues needing attention, fitting into three general categories: induction models; electrostimulation models; and human exposure limits. Of these, 9 were voted as 'high priority' by members of Subcommittee 6. The list is presented as a research agenda for refinements in numerical modeling with applications to human exposure limits. It is likely that such issues are also important in medical and electrical product safety design applications.

Survey of numerical electrostimulation models

This paper evaluates results of a survey of electrostimulation models of myelinated nerve. Participants were asked to determine thresholds of excitation for 18 cases involving different characteristics of the neuron, the stimulation waveform, and the electrode arrangement. Responses were received from 7 investigators using 10 models. Excitation thresholds differed significantly among these models. For example, with a 2 ms monophasic stimulus pulse and an electrode/fiber distance of 1 cm, thresholds from the least to greatest value differed by a factor of 8.3; with a 5 μs pulse, thresholds differed by the factor 3.8. Significant differences in reported simulations point to the need for experimental validation. Additional efforts are needed to develop computational models for unmyelinated C-fibers, A-delta fibers, CNS neurons, and CNS Synapses.

Investigation of assumptions underlying current safety guidelines on EM-induced nerve stimulation

An intricate network of a variety of nerves is embedded within the complex anatomy of the human body. Although nerves are shielded from unwanted excitation, they can still be stimulated by external electromagnetic sources that induce strongly non-uniform field distributions. Current exposure safety standards designed to limit unwanted nerve stimulation are based on a series of explicit and implicit assumptions and simplifications. This paper demonstrates the applicability of functionalized anatomical phantoms with integrated coupled electromagnetic and neuronal dynamics solvers for investigating the impact of magnetic resonance exposure on nerve excitation within the full complexity of the human anatomy. The impact of neuronal dynamics models, temperature and local hot-spots, nerve trajectory and potential smoothing, anatomical inhomogeneity, and pulse duration on nerve stimulation was evaluated. As a result, multiple assumptions underlying current safety standards are questioned. It is demonstrated that coupled EM-neuronal dynamics modeling involving realistic anatomies is valuable to establish conservative safety criteria.

Cauda equina conduction time in Guillain-Barré syndrome

The proximal segment of peripheral nerves is assumed to be involved in both demyelinating and axonal types of Guillain-Barré syndrome (GBS). However, electrophysiological examinations have not yet clarified if this segment is involved. We measured cauda equina conduction time (CECT) in nine demyelinating GBS and seven axonal GBS patients. Compound muscle action potentials (CMAPs) were recorded from the abductor hallucis muscle. Electrical stimulation was given at the ankle and the knee, and magnetic stimulation was given over the first sacral (S1) and first lumbar (L1) spinous processes using a magnetic augmented translumbosacral stimulation (MATS) coil. CECT was obtained by subtracting S1-level latency from L1-level latency. CECT was prolonged in all the patients with demyelinating GBS who had leg symptoms, whereas motor conduction velocity (MCV) at the peripheral nerve trunk was normal in all the patients. In all the patients with axonal GBS having leg symptoms, CECT and MCV were normal and no conduction blocks were detected between the ankle and the neuro-foramina. The cauda equina is much more frequently involved than the peripheral nerve trunk in demyelinating GBS. In axonal GBS, usually, CECT is normal and segmental lesions are absent between the ankle and the neuro-foramina. Therefore, the CECT measurement should be very useful for directly detecting demyelinating lesions in GBS.

Non-invasive electrical and magnetic stimulation of the brain, spinal cord, roots and peripheral nerves: Basic principles and procedures for routine clinical and research application. An updated report from an I.F.C.N. Committee

These guidelines provide an up-date of previous IFCN report on “Non-invasive electrical and magnetic stimulation of the brain, spinal cord and roots: basic principles and procedures for routine clinical application” (Rossini et al., 1994). A new Committee, composed of international experts, some of whom were in the panel of the 1994 “Report”, was selected to produce a current state-of-the-art review of non-invasive stimulation both for clinical application and research in neuroscience.

Since 1994, the international scientific community has seen a rapid increase in non-invasive brain stimulation in studying cognition, brain–behavior relationship and pathophysiology of various neurologic and psychiatric disorders. New paradigms of stimulation and new techniques have been developed. Furthermore, a large number of studies and clinical trials have demonstrated potential therapeutic applications of non-invasive brain stimulation, especially for TMS. Recent guidelines can be found in the literature covering specific aspects of non-invasive brain stimulation, such as safety (Rossi et al., 2009), methodology (Groppa et al., 2012) and therapeutic applications (Lefaucheur et al., 2014).

This up-dated review covers theoretical, physiological and practical aspects of non-invasive stimulation of brain, spinal cord, nerve roots and peripheral nerves in the light of more updated knowledge, and include some recent extensions and developments.